<p>This study investigates strategies for accelerating mosquito population replacement through the periodic release of <i>Wolbachia</i>-infected male mosquitoes using a two-dimensional time-switching model. We obtain the existence and stability of periodic solutions within this framework and establish several sufficient conditions for eradicating wild mosquitoes by varying the release amounts of infected males. Our results indicate that accelerated replacement is feasible as long as the <i>Wolbachia</i> infection is favorable. Despite <i>Wolbachia</i> infection brings a fitness costs, effective population replacement can still be achieved if the release waiting time does not exceed a certain threshold and the release amount is sufficient to match or surpass the capacity of wild mosquitoes. However, when the release waiting time exceeds this threshold, we identify a continuous, unbounded curve that separates two boundary equilibrium points, with solutions originating from either side converging to their respective boundary equilibrium points. Numerical simulations are presented to validate our theoretical findings, highlighting the potential of this approach for effective mosquito population control.</p>